Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 91x^{4} - 294x^{3} + 8292x^{2} - 17280x + 36864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.3 | ||
Root | \(-4.98253 - 8.62999i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.4.i.s.541.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.81683 | + | 17.0033i | 0.530059 | + | 0.918089i | 0.999385 | + | 0.0350644i | \(0.0111636\pi\) |
−0.469326 | + | 0.883025i | \(0.655503\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.5783 | + | 25.2504i | 0.399594 | + | 0.692117i | 0.993676 | − | 0.112288i | \(-0.0358179\pi\) |
−0.594082 | + | 0.804404i | \(0.702485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.81683 | − | 11.8071i | 0.145435 | − | 0.251900i | −0.784100 | − | 0.620634i | \(-0.786875\pi\) |
0.929535 | + | 0.368734i | \(0.120209\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 39.0460 | 0.557061 | 0.278531 | − | 0.960427i | \(-0.410153\pi\) | ||||
0.278531 | + | 0.960427i | \(0.410153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 43.7443 | 0.528192 | 0.264096 | − | 0.964496i | \(-0.414926\pi\) | ||||
0.264096 | + | 0.964496i | \(0.414926\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 79.6072 | − | 137.884i | 0.721706 | − | 1.25003i | −0.238610 | − | 0.971116i | \(-0.576692\pi\) |
0.960316 | − | 0.278916i | \(-0.0899751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.5725 | − | 21.7762i | −0.0805052 | − | 0.139439i | 0.822962 | − | 0.568097i | \(-0.192320\pi\) |
−0.903467 | + | 0.428658i | \(0.858987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.3686 | − | 101.097i | 0.338172 | − | 0.585730i | −0.645917 | − | 0.763407i | \(-0.723525\pi\) |
0.984089 | + | 0.177677i | \(0.0568583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −98.1683 | −0.474099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 329.383 | 1.46352 | 0.731759 | − | 0.681563i | \(-0.238700\pi\) | ||||
0.731759 | + | 0.681563i | \(0.238700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 90.4010 | − | 156.579i | 0.344348 | − | 0.596428i | −0.640887 | − | 0.767635i | \(-0.721433\pi\) |
0.985235 | + | 0.171207i | \(0.0547667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 106.836 | + | 185.046i | 0.378893 | + | 0.656261i | 0.990901 | − | 0.134590i | \(-0.0429716\pi\) |
−0.612009 | + | 0.790851i | \(0.709638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −89.7062 | − | 155.376i | −0.278404 | − | 0.482210i | 0.692584 | − | 0.721337i | \(-0.256472\pi\) |
−0.970988 | + | 0.239127i | \(0.923139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.2404 | + | 36.7895i | −0.0619255 | + | 0.107258i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −60.8635 | −0.157740 | −0.0788702 | − | 0.996885i | \(-0.525131\pi\) | ||||
−0.0788702 | + | 0.996885i | \(0.525131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −145.783 | −0.357407 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −191.289 | + | 331.322i | −0.422097 | + | 0.731093i | −0.996144 | − | 0.0877287i | \(-0.972039\pi\) |
0.574047 | + | 0.818822i | \(0.305372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −216.841 | − | 375.579i | −0.455142 | − | 0.788328i | 0.543555 | − | 0.839374i | \(-0.317078\pi\) |
−0.998696 | + | 0.0510454i | \(0.983745\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 34.0842 | + | 59.0355i | 0.0650403 | + | 0.112653i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62.5534 | + | 108.346i | −0.114061 | + | 0.197560i | −0.917404 | − | 0.397957i | \(-0.869719\pi\) |
0.803343 | + | 0.595517i | \(0.203053\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 30.0873 | 0.0502917 | 0.0251458 | − | 0.999684i | \(-0.491995\pi\) | ||||
0.0251458 | + | 0.999684i | \(0.491995\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 676.299 | 1.08431 | 0.542156 | − | 0.840278i | \(-0.317608\pi\) | ||||
0.542156 | + | 0.840278i | \(0.317608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −286.226 | + | 495.758i | −0.423617 | + | 0.733725i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 416.924 | + | 722.134i | 0.593768 | + | 1.02844i | 0.993719 | + | 0.111900i | \(0.0356936\pi\) |
−0.399952 | + | 0.916536i | \(0.630973\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −176.729 | − | 306.103i | −0.233717 | − | 0.404810i | 0.725182 | − | 0.688557i | \(-0.241756\pi\) |
−0.958899 | + | 0.283748i | \(0.908422\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −97.6149 | + | 169.074i | −0.124563 | + | 0.215749i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 948.224 | 1.12934 | 0.564671 | − | 0.825316i | \(-0.309003\pi\) | ||||
0.564671 | + | 0.825316i | \(0.309003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 267.679 | 0.308356 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −109.361 | + | 189.419i | −0.118107 | + | 0.204568i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 142.919 | + | 247.543i | 0.149600 | + | 0.259115i | 0.931080 | − | 0.364816i | \(-0.118868\pi\) |
−0.781480 | + | 0.623931i | \(0.785535\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −737.354 | − | 1277.13i | −0.726430 | − | 1.25821i | −0.958383 | − | 0.285487i | \(-0.907845\pi\) |
0.231952 | − | 0.972727i | \(-0.425489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −877.649 | + | 1520.13i | −0.839586 | + | 1.45421i | 0.0506558 | + | 0.998716i | \(0.483869\pi\) |
−0.890241 | + | 0.455489i | \(0.849464\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 657.811 | 0.594327 | 0.297164 | − | 0.954827i | \(-0.403959\pi\) | ||||
0.297164 | + | 0.954827i | \(0.403959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1042.07 | −0.915706 | −0.457853 | − | 0.889028i | \(-0.651381\pi\) | ||||
−0.457853 | + | 0.889028i | \(0.651381\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 281.763 | − | 488.028i | 0.234567 | − | 0.406281i | −0.724580 | − | 0.689191i | \(-0.757966\pi\) |
0.959147 | + | 0.282909i | \(0.0912996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 398.036 | + | 689.418i | 0.322757 | + | 0.559031i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 383.308 | + | 663.909i | 0.295275 | + | 0.511432i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 240.445 | − | 416.463i | 0.180650 | − | 0.312895i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 202.776 | 0.141681 | 0.0708406 | − | 0.997488i | \(-0.477432\pi\) | ||||
0.0708406 | + | 0.997488i | \(0.477432\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −555.945 | + | 962.926i | −0.370788 | + | 0.642223i | −0.989687 | − | 0.143247i | \(-0.954246\pi\) |
0.618899 | + | 0.785470i | \(0.287579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 429.431 | + | 743.796i | 0.279973 | + | 0.484927i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −272.703 | − | 472.335i | −0.170063 | − | 0.294557i | 0.768379 | − | 0.639995i | \(-0.221064\pi\) |
−0.938442 | + | 0.345438i | \(0.887730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 678.287 | − | 1174.83i | 0.413896 | − | 0.716889i | −0.581416 | − | 0.813606i | \(-0.697501\pi\) |
0.995312 | + | 0.0967178i | \(0.0308344\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 397.512 | 0.232459 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 125.725 | 0.0720061 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1736.30 | + | 3007.36i | −0.954653 | + | 1.65351i | −0.219494 | + | 0.975614i | \(0.570441\pi\) |
−0.735159 | + | 0.677894i | \(0.762893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1701.70 | + | 2947.43i | 0.917101 | + | 1.58847i | 0.803796 | + | 0.594905i | \(0.202810\pi\) |
0.113305 | + | 0.993560i | \(0.463856\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 291.843 | + | 505.487i | 0.151235 | + | 0.261947i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 181.097 | − | 313.669i | 0.0920579 | − | 0.159449i | −0.816319 | − | 0.577601i | \(-0.803989\pi\) |
0.908377 | + | 0.418152i | \(0.137322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3125.96 | 1.53019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1830.32 | 0.879520 | 0.439760 | − | 0.898115i | \(-0.355063\pi\) | ||||
0.439760 | + | 0.898115i | \(0.355063\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 417.759 | − | 723.580i | 0.193576 | − | 0.335283i | −0.752857 | − | 0.658184i | \(-0.771325\pi\) |
0.946433 | + | 0.322901i | \(0.104658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1005.56 | + | 1741.68i | 0.457698 | + | 0.792755i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −859.902 | − | 1489.39i | −0.377903 | − | 0.654547i | 0.612854 | − | 0.790196i | \(-0.290021\pi\) |
−0.990757 | + | 0.135649i | \(0.956688\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 245.421 | − | 425.081i | 0.106012 | − | 0.183618i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2291.42 | −0.956809 | −0.478404 | − | 0.878140i | \(-0.658785\pi\) | ||||
−0.478404 | + | 0.878140i | \(0.658785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4228.30 | 1.73639 | 0.868197 | − | 0.496221i | \(-0.165279\pi\) | ||||
0.868197 | + | 0.496221i | \(0.165279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −823.457 | + | 1426.27i | −0.327253 | + | 0.566818i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 569.225 | + | 985.926i | 0.222598 | + | 0.385551i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1023.22 | − | 1772.27i | −0.387632 | − | 0.671398i | 0.604499 | − | 0.796606i | \(-0.293373\pi\) |
−0.992131 | + | 0.125208i | \(0.960040\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −548.462 | + | 949.964i | −0.204555 | + | 0.354300i | −0.949991 | − | 0.312277i | \(-0.898908\pi\) |
0.745436 | + | 0.666578i | \(0.232241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1593.40 | 0.576269 | 0.288135 | − | 0.957590i | \(-0.406965\pi\) | ||||
0.288135 | + | 0.957590i | \(0.406965\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4936.25 | 1.75840 | 0.879201 | − | 0.476452i | \(-0.158077\pi\) | ||||
0.879201 | + | 0.476452i | \(0.158077\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 246.844 | − | 427.546i | 0.0853451 | − | 0.147822i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 452.005 | + | 782.896i | 0.153997 | + | 0.266731i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 637.719 | + | 1104.56i | 0.211062 | + | 0.365570i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −664.709 | + | 1151.31i | −0.216874 | + | 0.375637i | −0.953851 | − | 0.300281i | \(-0.902919\pi\) |
0.736977 | + | 0.675918i | \(0.236253\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1068.36 | −0.338892 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2291.98 | 0.717004 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 266.170 | − | 461.020i | 0.0810159 | − | 0.140324i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 512.410 | + | 887.520i | 0.153872 | + | 0.266515i | 0.932648 | − | 0.360788i | \(-0.117492\pi\) |
−0.778776 | + | 0.627303i | \(0.784159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −266.844 | − | 462.188i | −0.0780224 | − | 0.135139i | 0.824374 | − | 0.566045i | \(-0.191527\pi\) |
−0.902397 | + | 0.430906i | \(0.858194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.5468 | − | 44.2484i | 0.00737198 | − | 0.0127686i | −0.862316 | − | 0.506371i | \(-0.830987\pi\) |
0.869688 | + | 0.493602i | \(0.164320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 509.227 | 0.143178 | 0.0715892 | − | 0.997434i | \(-0.477193\pi\) | ||||
0.0715892 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 897.062 | 0.249012 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1392.38 | + | 2411.67i | −0.376843 | + | 0.652711i | −0.990601 | − | 0.136783i | \(-0.956324\pi\) |
0.613758 | + | 0.789494i | \(0.289657\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 41.5097 | + | 71.8969i | 0.0110949 | + | 0.0192170i | 0.871520 | − | 0.490361i | \(-0.163135\pi\) |
−0.860425 | + | 0.509578i | \(0.829802\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −106.202 | − | 183.948i | −0.0276939 | − | 0.0479673i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 298.198 | − | 516.494i | 0.0768173 | − | 0.133052i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1286.35 | 0.323480 | 0.161740 | − | 0.986833i | \(-0.448289\pi\) | ||||
0.161740 | + | 0.986833i | \(0.448289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4642.16 | 1.15356 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −772.063 | + | 1337.25i | −0.187393 | + | 0.324574i | −0.944380 | − | 0.328856i | \(-0.893337\pi\) |
0.756987 | + | 0.653429i | \(0.226670\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3233.49 | + | 5600.58i | 0.775751 | + | 1.34364i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4161.79 | − | 7208.43i | −0.975767 | − | 1.69008i | −0.677380 | − | 0.735634i | \(-0.736884\pi\) |
−0.298388 | − | 0.954445i | \(-0.596449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 152.159 | − | 263.547i | 0.0352718 | − | 0.0610926i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3203.80 | 0.726168 | 0.363084 | − | 0.931756i | \(-0.381724\pi\) | ||||
0.363084 | + | 0.931756i | \(0.381724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1419.39 | −0.318161 | −0.159081 | − | 0.987266i | \(-0.550853\pi\) | ||||
−0.159081 | + | 0.987266i | \(0.550853\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 364.458 | − | 631.260i | 0.0799187 | − | 0.138423i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4438.45 | + | 7687.62i | 0.962745 | + | 1.66752i | 0.715555 | + | 0.698557i | \(0.246174\pi\) |
0.247191 | + | 0.968967i | \(0.420493\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1303.27 | + | 2257.33i | 0.276679 | + | 0.479221i | 0.970557 | − | 0.240871i | \(-0.0774329\pi\) |
−0.693879 | + | 0.720092i | \(0.744100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −703.389 | + | 1218.31i | −0.147746 | + | 0.255904i | −0.930394 | − | 0.366561i | \(-0.880535\pi\) |
0.782648 | + | 0.622465i | \(0.213869\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3549.81 | 0.730099 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3388.41 | −0.689683 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3585.00 | + | 6209.41i | −0.714806 | + | 1.23808i | 0.248229 | + | 0.968701i | \(0.420152\pi\) |
−0.963034 | + | 0.269378i | \(0.913182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −956.445 | − | 1656.61i | −0.188767 | − | 0.326955i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1085.34 | − | 1879.86i | −0.209922 | − | 0.363596i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2097.59 | + | 3633.13i | −0.401671 | + | 0.695715i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2168.41 | 0.407091 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3695.22 | 0.686963 | 0.343481 | − | 0.939160i | \(-0.388394\pi\) | ||||
0.343481 | + | 0.939160i | \(0.388394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3042.83 | − | 5270.34i | 0.554801 | − | 0.960944i | −0.443118 | − | 0.896463i | \(-0.646128\pi\) |
0.997919 | − | 0.0644805i | \(-0.0205390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −887.284 | − | 1536.82i | −0.160231 | − | 0.277528i | 0.774721 | − | 0.632304i | \(-0.217891\pi\) |
−0.934951 | + | 0.354776i | \(0.884557\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4176.76 | − | 7234.37i | −0.740033 | − | 1.28177i | −0.952480 | − | 0.304602i | \(-0.901477\pi\) |
0.212447 | − | 0.977173i | \(-0.431857\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 366.572 | − | 634.921i | 0.0643388 | − | 0.111438i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1708.04 | 0.294235 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −340.842 | −0.0581738 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1761.26 | − | 3050.59i | 0.295141 | − | 0.511199i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1892.90 | + | 3278.60i | 0.314330 | + | 0.544436i | 0.979295 | − | 0.202439i | \(-0.0648867\pi\) |
−0.664965 | + | 0.746875i | \(0.731553\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −312.767 | − | 541.728i | −0.0510098 | − | 0.0883516i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3731.54 | + | 6463.22i | −0.603176 | + | 1.04473i | 0.389161 | + | 0.921170i | \(0.372765\pi\) |
−0.992337 | + | 0.123561i | \(0.960569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3403.67 | 0.540525 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5900.29 | 0.928822 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1710.53 | + | 2962.73i | −0.264629 | + | 0.458350i | −0.967466 | − | 0.253000i | \(-0.918583\pi\) |
0.702838 | + | 0.711350i | \(0.251916\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1300.41 | + | 2252.37i | 0.199453 | + | 0.345463i | 0.948351 | − | 0.317222i | \(-0.102750\pi\) |
−0.748898 | + | 0.662685i | \(0.769417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1108.89 | + | 1920.65i | 0.167196 | + | 0.289592i | 0.937433 | − | 0.348166i | \(-0.113195\pi\) |
−0.770237 | + | 0.637758i | \(0.779862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −75.2183 | + | 130.282i | −0.0112456 | + | 0.0194779i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10423.6 | 1.53241 | 0.766207 | − | 0.642594i | \(-0.222142\pi\) | ||||
0.766207 | + | 0.642594i | \(0.222142\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4945.43 | −0.721014 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1690.75 | + | 2928.46i | −0.242460 | + | 0.419953i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.9681 | − | 27.6576i | −0.00227120 | − | 0.00393383i | 0.864888 | − | 0.501966i | \(-0.167390\pi\) |
−0.867159 | + | 0.498032i | \(0.834056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −597.487 | − | 1034.88i | −0.0836118 | − | 0.144820i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −116.674 | + | 202.086i | −0.0161961 | + | 0.0280526i | −0.874010 | − | 0.485908i | \(-0.838489\pi\) |
0.857814 | + | 0.513961i | \(0.171822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −342.818 | −0.0468330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5558.90 | 0.753408 | 0.376704 | − | 0.926334i | \(-0.377057\pi\) | ||||
0.376704 | + | 0.926334i | \(0.377057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4082.12 | + | 7070.44i | −0.544613 | + | 0.943297i | 0.454019 | + | 0.890992i | \(0.349990\pi\) |
−0.998631 | + | 0.0523045i | \(0.983343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1431.13 | − | 2478.79i | −0.189447 | − | 0.328132i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5098.55 | − | 8830.95i | −0.664542 | − | 1.15102i | −0.979409 | − | 0.201884i | \(-0.935293\pi\) |
0.314868 | − | 0.949136i | \(-0.398040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3108.34 | − | 5383.80i | 0.402034 | − | 0.696344i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4169.24 | −0.531082 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2601.86 | −0.328926 | −0.164463 | − | 0.986383i | \(-0.552589\pi\) | ||||
−0.164463 | + | 0.986383i | \(0.552589\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2592.64 | + | 4490.58i | −0.322868 | + | 0.559224i | −0.981079 | − | 0.193610i | \(-0.937980\pi\) |
0.658211 | + | 0.752834i | \(0.271314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −795.779 | − | 1378.33i | −0.0983637 | − | 0.170371i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4801.85 | + | 8317.04i | 0.584813 | + | 1.01293i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3591.73 | + | 6221.06i | −0.434229 | + | 0.752107i | −0.997232 | − | 0.0743476i | \(-0.976313\pi\) |
0.563003 | + | 0.826455i | \(0.309646\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7511.41 | −0.894945 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1767.29 | 0.209043 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −341.614 | + | 591.693i | −0.0398304 | + | 0.0689883i | −0.885253 | − | 0.465109i | \(-0.846015\pi\) |
0.845423 | + | 0.534097i | \(0.179348\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5372.54 | + | 9305.51i | 0.621951 | + | 1.07725i | 0.989122 | + | 0.147098i | \(0.0469932\pi\) |
−0.367171 | + | 0.930154i | \(0.619674\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −488.075 | − | 845.370i | −0.0557061 | − | 0.0964858i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4257.38 | − | 7374.00i | 0.482504 | − | 0.835721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1055.60 | −0.117974 | −0.0589869 | − | 0.998259i | \(-0.518787\pi\) | ||||
−0.0589869 | + | 0.998259i | \(0.518787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4536.95 | −0.503538 | −0.251769 | − | 0.967787i | \(-0.581012\pi\) | ||||
−0.251769 | + | 0.967787i | \(0.581012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3482.36 | − | 6031.63i | 0.381199 | − | 0.660256i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3783.93 | − | 6553.95i | −0.411383 | − | 0.712536i | 0.583659 | − | 0.811999i | \(-0.301621\pi\) |
−0.995041 | + | 0.0994636i | \(0.968287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5172.57 | + | 8959.15i | 0.554754 | + | 0.960863i | 0.997923 | + | 0.0644244i | \(0.0205211\pi\) |
−0.443168 | + | 0.896439i | \(0.646146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2370.56 | + | 4105.93i | −0.252529 | + | 0.437393i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11122.4 | −1.16904 | −0.584520 | − | 0.811379i | \(-0.698717\pi\) | ||||
−0.584520 | + | 0.811379i | \(0.698717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5271.58 | 0.550397 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −669.197 | + | 1159.08i | −0.0689504 | + | 0.119426i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 869.224 | + | 1505.54i | 0.0889728 | + | 0.154105i | 0.907077 | − | 0.420964i | \(-0.138308\pi\) |
−0.818104 | + | 0.575070i | \(0.804975\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3786.38 | + | 6558.20i | 0.382536 | + | 0.662572i | 0.991424 | − | 0.130684i | \(-0.0417174\pi\) |
−0.608888 | + | 0.793256i | \(0.708384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6358.96 | − | 11014.0i | 0.638285 | − | 1.10554i | −0.347525 | − | 0.937671i | \(-0.612978\pi\) |
0.985809 | − | 0.167870i | \(-0.0536890\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4641.96 | −0.459967 | −0.229983 | − | 0.973195i | \(-0.573867\pi\) | ||||
−0.229983 | + | 0.973195i | \(0.573867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2456.31 | −0.241837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3114.99 | + | 5395.32i | −0.302806 | + | 0.524476i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −546.804 | − | 947.093i | −0.0528192 | − | 0.0914855i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2817.98 | + | 4880.89i | 0.268804 | + | 0.465581i | 0.968553 | − | 0.248807i | \(-0.0800384\pi\) |
−0.699750 | + | 0.714388i | \(0.746705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2245.35 | − | 3889.05i | 0.212846 | − | 0.368660i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1429.19 | −0.133807 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1557.90 | −0.144960 | −0.0724799 | − | 0.997370i | \(-0.523091\pi\) | ||||
−0.0724799 | + | 0.997370i | \(0.523091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3374.51 | − | 5844.83i | 0.310162 | − | 0.537217i | −0.668235 | − | 0.743950i | \(-0.732950\pi\) |
0.978397 | + | 0.206733i | \(0.0662833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −490.905 | − | 850.272i | −0.0448463 | − | 0.0776761i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 295.362 | + | 511.582i | 0.0266576 | + | 0.0461722i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1114.74 | + | 1930.79i | −0.100005 | + | 0.173214i | −0.911687 | − | 0.410886i | \(-0.865219\pi\) |
0.811681 | + | 0.584101i | \(0.198553\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13685.7 | −1.21315 | −0.606577 | − | 0.795024i | \(-0.707458\pi\) | ||||
−0.606577 | + | 0.795024i | \(0.707458\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7373.54 | 0.649739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6813.72 | − | 11801.7i | 0.593346 | − | 1.02770i | −0.400432 | − | 0.916326i | \(-0.631140\pi\) |
0.993778 | − | 0.111379i | \(-0.0355266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6639.12 | + | 11499.3i | 0.574750 | + | 0.995496i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4388.24 | − | 7600.66i | −0.375474 | − | 0.650340i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2615.53 | − | 4530.23i | 0.222497 | − | 0.385376i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21425.1 | 1.80163 | 0.900817 | − | 0.434200i | \(-0.142969\pi\) | ||||
0.900817 | + | 0.434200i | \(0.142969\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8954.62 | 0.748677 | 0.374338 | − | 0.927292i | \(-0.377870\pi\) | ||||
0.374338 | + | 0.927292i | \(0.377870\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2279.06 | − | 3947.45i | 0.188382 | − | 0.326288i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6591.10 | − | 11416.1i | −0.541719 | − | 0.938285i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1232.50 | − | 2134.75i | −0.100160 | − | 0.173483i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1644.53 | + | 2848.41i | −0.132896 | + | 0.230182i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1238.60 | −0.0989801 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10982.6 | −0.872788 | −0.436394 | − | 0.899756i | \(-0.643745\pi\) | ||||
−0.436394 | + | 0.899756i | \(0.643745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2605.17 | − | 4512.28i | 0.204758 | − | 0.354651i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7606.61 | − | 13175.0i | −0.594580 | − | 1.02984i | −0.993606 | − | 0.112903i | \(-0.963985\pi\) |
0.399026 | − | 0.916940i | \(-0.369348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −549.975 | − | 952.585i | −0.0425222 | − | 0.0736506i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8185.75 | + | 14178.1i | −0.629464 | + | 1.09026i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12732.7 | 0.968588 | 0.484294 | − | 0.874905i | \(-0.339077\pi\) | ||||
0.484294 | + | 0.874905i | \(0.339077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2913.14 | 0.220416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5444.61 | + | 9430.34i | −0.407572 | + | 0.705935i | −0.994617 | − | 0.103619i | \(-0.966958\pi\) |
0.587045 | + | 0.809554i | \(0.300291\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1408.81 | + | 2440.14i | 0.104901 | + | 0.181694i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 784.009 | + | 1357.94i | 0.0577634 | + | 0.100049i | 0.893461 | − | 0.449141i | \(-0.148270\pi\) |
−0.835698 | + | 0.549190i | \(0.814936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12209.1 | − | 21146.8i | 0.894809 | − | 1.54986i | 0.0607693 | − | 0.998152i | \(-0.480645\pi\) |
0.834040 | − | 0.551704i | \(-0.186022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3980.36 | −0.288682 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21305.8 | −1.53721 | −0.768606 | − | 0.639722i | \(-0.779049\pi\) | ||||
−0.768606 | + | 0.639722i | \(0.779049\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3469.83 | − | 6009.93i | 0.247768 | − | 0.429146i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −887.288 | − | 1536.83i | −0.0630321 | − | 0.109175i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12731.5 | + | 22051.5i | 0.895202 | + | 1.55054i | 0.833554 | + | 0.552437i | \(0.186302\pi\) |
0.0616476 | + | 0.998098i | \(0.480365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2553.30 | − | 4422.44i | 0.178619 | − | 0.309378i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26914.5 | −1.86382 | −0.931911 | − | 0.362686i | \(-0.881860\pi\) | ||||
−0.931911 | + | 0.362686i | \(0.881860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3833.08 | −0.264102 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10476.2 | − | 18145.4i | 0.714604 | − | 1.23773i | −0.248509 | − | 0.968630i | \(-0.579940\pi\) |
0.963112 | − | 0.269100i | \(-0.0867262\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12895.9 | − | 22336.3i | −0.875265 | − | 1.51600i | −0.856480 | − | 0.516180i | \(-0.827354\pi\) |
−0.0187845 | − | 0.999824i | \(-0.505980\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1202.22 | + | 2082.31i | 0.0807890 | + | 0.139931i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3268.48 | − | 5661.18i | 0.218556 | − | 0.378551i | −0.735810 | − | 0.677188i | \(-0.763199\pi\) |
0.954367 | + | 0.298637i | \(0.0965319\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2446.05 | −0.161958 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22102.9 | −1.45633 | −0.728163 | − | 0.685404i | \(-0.759626\pi\) | ||||
−0.728163 | + | 0.685404i | \(0.759626\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1393.97 | − | 2414.43i | 0.0909549 | − | 0.157539i | −0.816958 | − | 0.576697i | \(-0.804341\pi\) |
0.907913 | + | 0.419158i | \(0.137675\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3901.30 | − | 6757.24i | −0.253322 | − | 0.438767i | 0.711116 | − | 0.703074i | \(-0.248190\pi\) |
−0.964438 | + | 0.264308i | \(0.914857\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9308.55 | + | 16122.9i | 0.598618 | + | 1.03684i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12861.1 | 0.815269 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18267.8 | −1.15251 | −0.576253 | − | 0.817272i | \(-0.695486\pi\) | ||||
−0.576253 | + | 0.817272i | \(0.695486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −506.941 | + | 878.048i | −0.0316809 | + | 0.0548729i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 289.585 | + | 501.576i | 0.0180122 | + | 0.0311981i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1804.48 | + | 3125.46i | 0.111190 | + | 0.192587i | 0.916250 | − | 0.400606i | \(-0.131200\pi\) |
−0.805060 | + | 0.593193i | \(0.797867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9925.67 | + | 17191.8i | −0.608756 | + | 1.05440i | 0.382690 | + | 0.923877i | \(0.374998\pi\) |
−0.991446 | + | 0.130520i | \(0.958335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9352.11 | 0.568268 | 0.284134 | − | 0.958785i | \(-0.408294\pi\) | ||||
0.284134 | + | 0.958785i | \(0.408294\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11154.7 | −0.674669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13108.3 | + | 22704.2i | −0.785553 | + | 1.36062i | 0.143115 | + | 0.989706i | \(0.454288\pi\) |
−0.928668 | + | 0.370912i | \(0.879045\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2779.73 | − | 4814.63i | −0.165821 | − | 0.287211i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7691.89 | − | 13322.8i | −0.454679 | − | 0.787528i | 0.543990 | − | 0.839091i | \(-0.316913\pi\) |
−0.998670 | + | 0.0515638i | \(0.983579\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6855.48 | + | 11874.0i | −0.403400 | + | 0.698709i | −0.994134 | − | 0.108157i | \(-0.965505\pi\) |
0.590734 | + | 0.806866i | \(0.298838\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4294.31 | −0.250415 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4003.44 | −0.232404 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6322.35 | − | 10950.6i | 0.363743 | − | 0.630022i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13898.4 | − | 24072.7i | −0.796054 | − | 1.37881i | −0.922168 | − | 0.386790i | \(-0.873584\pi\) |
0.126114 | − | 0.992016i | \(-0.459749\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14296.7 | − | 24762.6i | −0.811621 | − | 1.40577i | −0.911729 | − | 0.410792i | \(-0.865252\pi\) |
0.100108 | − | 0.994977i | \(-0.468081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2806.02 | + | 4860.18i | −0.158594 | + | 0.274693i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33510.5 | −1.87737 | −0.938686 | − | 0.344774i | \(-0.887956\pi\) | ||||
−0.938686 | + | 0.344774i | \(0.887956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2727.03 | 0.152109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −414.896 | + | 718.622i | −0.0229409 | + | 0.0397348i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4784.99 | − | 8287.84i | −0.263429 | − | 0.456273i | 0.703722 | − | 0.710476i | \(-0.251520\pi\) |
−0.967151 | + | 0.254203i | \(0.918187\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3391.43 | + | 5874.13i | 0.185100 | + | 0.320602i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3529.79 | − | 6113.78i | 0.191823 | − | 0.332247i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6945.59 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14408.6 | 0.773018 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14477.0 | − | 25074.8i | 0.770102 | − | 1.33386i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2969.13 | − | 5142.68i | −0.157275 | − | 0.272408i | 0.776610 | − | 0.629982i | \(-0.216938\pi\) |
−0.933885 | + | 0.357573i | \(0.883604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9293.12 | − | 16096.2i | −0.488121 | − | 0.845450i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −993.780 | + | 1721.28i | −0.0519794 | + | 0.0900310i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7669.30 | −0.397798 | −0.198899 | − | 0.980020i | \(-0.563737\pi\) | ||||
−0.198899 | + | 0.980020i | \(0.563737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34462.9 | −1.78012 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −314.312 | + | 544.405i | −0.0161010 | + | 0.0278878i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3929.73 | − | 6806.50i | −0.200476 | − | 0.347234i | 0.748206 | − | 0.663466i | \(-0.230915\pi\) |
−0.948682 | + | 0.316232i | \(0.897582\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4171.53 | + | 7225.30i | 0.211066 | + | 0.365578i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15104.4 | + | 26161.6i | −0.761111 | + | 1.31828i | 0.181167 | + | 0.983452i | \(0.442013\pi\) |
−0.942278 | + | 0.334831i | \(0.891321\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3647.70 | −0.182313 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6648.76 | 0.330959 | 0.165480 | − | 0.986213i | \(-0.447083\pi\) | ||||
0.165480 | + | 0.986213i | \(0.447083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3823.34 | − | 6622.22i | 0.188782 | − | 0.326979i | −0.756063 | − | 0.654499i | \(-0.772879\pi\) |
0.944844 | + | 0.327520i | \(0.106213\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8681.51 | − | 15036.8i | −0.426934 | − | 0.739471i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6457.62 | + | 11184.9i | 0.315029 | + | 0.545646i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15813.4 | − | 27389.7i | 0.768363 | − | 1.33084i | −0.170088 | − | 0.985429i | \(-0.554405\pi\) |
0.938450 | − | 0.345414i | \(-0.112262\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17017.0 | −0.820280 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6859.10 | −0.329324 | −0.164662 | − | 0.986350i | \(-0.552653\pi\) | ||||
−0.164662 | + | 0.986350i | \(0.552653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8989.30 | − | 15569.9i | 0.428202 | − | 0.741668i | −0.568511 | − | 0.822676i | \(-0.692480\pi\) |
0.996714 | + | 0.0810073i | \(0.0258137\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10229.8 | − | 17718.5i | −0.485378 | − | 0.840700i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2607.97 | + | 4517.14i | 0.122775 | + | 0.212652i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7584.52 | − | 13136.8i | 0.355663 | − | 0.616027i | −0.631568 | − | 0.775320i | \(-0.717588\pi\) |
0.987231 | + | 0.159294i | \(0.0509217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2921.73 | −0.135947 | −0.0679736 | − | 0.997687i | \(-0.521653\pi\) | ||||
−0.0679736 | + | 0.997687i | \(0.521653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2918.43 | −0.135269 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3954.53 | − | 6849.45i | 0.181882 | − | 0.315028i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 438.623 | + | 759.717i | 0.0200962 | + | 0.0348077i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 905.483 | + | 1568.34i | 0.0411695 | + | 0.0713077i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8027.38 | + | 13903.8i | −0.363590 | + | 0.629756i | −0.988549 | − | 0.150901i | \(-0.951782\pi\) |
0.624959 | + | 0.780658i | \(0.285116\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11064.1 | 0.497337 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5912.67 | −0.264773 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8717.49 | + | 15099.1i | −0.387440 | + | 0.671065i | −0.992104 | − | 0.125415i | \(-0.959974\pi\) |
0.604665 | + | 0.796480i | \(0.293307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3502.66 | − | 6066.79i | −0.155088 | − | 0.268620i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9859.31 | + | 17076.8i | 0.433285 | + | 0.750471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7814.90 | + | 13535.8i | −0.342160 | + | 0.592639i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22185.0 | −0.964132 | −0.482066 | − | 0.876135i | \(-0.660113\pi\) | ||||
−0.482066 | + | 0.876135i | \(0.660113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18738.5 | −0.811341 | −0.405671 | − | 0.914019i | \(-0.632962\pi\) | ||||
−0.405671 | + | 0.914019i | \(0.632962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4575.80 | + | 7925.52i | −0.196667 | + | 0.340637i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4673.48 | + | 8094.71i | 0.200128 | + | 0.346632i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8204.34 | + | 14210.3i | 0.348762 | + | 0.604073i | 0.986030 | − | 0.166569i | \(-0.0532689\pi\) |
−0.637268 | + | 0.770642i | \(0.719936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3908.12 | − | 6769.06i | 0.165527 | − | 0.286701i | −0.771315 | − | 0.636453i | \(-0.780401\pi\) |
0.936842 | + | 0.349752i | \(0.113734\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12444.2 | 0.523248 | 0.261624 | − | 0.965170i | \(-0.415742\pi\) | ||||
0.261624 | + | 0.965170i | \(0.415742\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21850.1 | −0.915422 | −0.457711 | − | 0.889101i | \(-0.651331\pi\) | ||||
−0.457711 | + | 0.889101i | \(0.651331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −829.353 | + | 1436.48i | −0.0344963 | + | 0.0597493i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2088.79 | + | 3617.90i | 0.0865697 | + | 0.149943i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19445.7 | + | 33680.9i | 0.800166 | + | 1.38593i | 0.919506 | + | 0.393075i | \(0.128589\pi\) |
−0.119340 | + | 0.992853i | \(0.538078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11878.4 | − | 20573.9i | 0.487038 | − | 0.843574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10055.6 | −0.409377 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9441.63 | 0.383020 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26221.2 | − | 45416.5i | 1.05623 | − | 1.82944i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14665.7 | − | 25401.8i | −0.588680 | − | 1.01962i | −0.994406 | − | 0.105629i | \(-0.966314\pi\) |
0.405725 | − | 0.913995i | \(-0.367019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7009.11 | + | 12140.1i | 0.279377 | + | 0.483896i | 0.971230 | − | 0.238143i | \(-0.0765386\pi\) |
−0.691853 | + | 0.722039i | \(0.743205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3908.31 | − | 6769.40i | 0.155239 | − | 0.268881i | −0.777907 | − | 0.628379i | \(-0.783719\pi\) |
0.933146 | + | 0.359498i | \(0.117052\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39764.9 | −1.56850 | −0.784248 | − | 0.620448i | \(-0.786951\pi\) | ||||
−0.784248 | + | 0.620448i | \(0.786951\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8599.02 | 0.338006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12156.1 | + | 21055.0i | −0.474532 | + | 0.821913i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 852.832 | + | 1477.15i | 0.0331769 | + | 0.0574642i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1227.10 | + | 2125.41i | 0.0474099 | + | 0.0821164i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18359.0 | − | 31798.7i | 0.706887 | − | 1.22436i | −0.259119 | − | 0.965845i | \(-0.583432\pi\) |
0.966006 | − | 0.258519i | \(-0.0832344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49326.5 | 1.88633 | 0.943163 | − | 0.332331i | \(-0.107835\pi\) | ||||
0.943163 | + | 0.332331i | \(0.107835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32093.1 | 1.22312 | 0.611562 | − | 0.791197i | \(-0.290542\pi\) | ||||
0.611562 | + | 0.791197i | \(0.290542\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10575.4 | − | 18317.2i | 0.400324 | − | 0.693382i | −0.593441 | − | 0.804878i | \(-0.702231\pi\) |
0.993765 | + | 0.111496i | \(0.0355642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1990.62 | + | 3447.86i | 0.0750994 | + | 0.130076i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3924.14 | − | 6796.81i | −0.147051 | − | 0.254699i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5728.55 | − | 9922.14i | 0.213949 | − | 0.370570i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2935.36 | −0.108898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2376.47 | −0.0878711 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10570.8 | + | 18309.1i | −0.388269 | + | 0.672502i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8791.29 | + | 15227.0i | 0.321841 | + | 0.557445i | 0.980868 | − | 0.194674i | \(-0.0623649\pi\) |
−0.659027 | + | 0.752119i | \(0.729032\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6849.45 | + | 11863.6i | 0.249102 | + | 0.431458i | 0.963277 | − | 0.268510i | \(-0.0865311\pi\) |
−0.714175 | + | 0.699968i | \(0.753198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5152.82 | − | 8924.95i | 0.186784 | − | 0.323519i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21830.5 | −0.786157 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14632.7 | −0.525231 | −0.262616 | − | 0.964901i | \(-0.584585\pi\) | ||||
−0.262616 | + | 0.964901i | \(0.584585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 205.100 | − | 355.244i | 0.00731415 | − | 0.0126685i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4117.28 | − | 7131.34i | −0.146352 | − | 0.253489i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7531.24 | − | 13044.5i | −0.265976 | − | 0.460685i | 0.701843 | − | 0.712332i | \(-0.252361\pi\) |
−0.967819 | + | 0.251647i | \(0.919028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −929.149 | + | 1609.33i | −0.0327085 | + | 0.0566528i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5692.25 | −0.199098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52963.9 | −1.84659 | −0.923296 | − | 0.384090i | \(-0.874515\pi\) | ||||
−0.923296 | + | 0.384090i | \(0.874515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12431.0 | − | 21531.1i | 0.430647 | − | 0.745903i | −0.566282 | − | 0.824212i | \(-0.691619\pi\) |
0.996929 | + | 0.0783086i | \(0.0249520\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14393.1 | − | 24929.6i | −0.497036 | − | 0.860891i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14898.2 | + | 25804.4i | 0.511221 | + | 0.885461i | 0.999915 | + | 0.0130059i | \(0.00414002\pi\) |
−0.488694 | + | 0.872455i | \(0.662527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4610.22 | − | 7985.13i | 0.157697 | − | 0.273138i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10042.2 | −0.341341 | −0.170670 | − | 0.985328i | \(-0.554593\pi\) | ||||
−0.170670 | + | 0.985328i | \(0.554593\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10232.2 | 0.346708 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5354.16 | − | 9273.68i | 0.180287 | − | 0.312266i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8081.70 | + | 13997.9i | 0.271280 | + | 0.469871i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2742.31 | − | 4749.82i | −0.0914799 | − | 0.158448i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12537.7 | − | 21716.0i | 0.416945 | − | 0.722170i | −0.578686 | − | 0.815551i | \(-0.696434\pi\) |
0.995630 | + | 0.0933811i | \(0.0297675\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6632.06 | −0.219189 | −0.109595 | − | 0.993976i | \(-0.534955\pi\) | ||||
−0.109595 | + | 0.993976i | \(0.534955\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26634.5 | 0.877557 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20484.0 | − | 35479.3i | 0.670768 | − | 1.16180i | −0.306919 | − | 0.951736i | \(-0.599298\pi\) |
0.977687 | − | 0.210069i | \(-0.0673687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13823.5 | + | 23943.0i | 0.451278 | + | 0.781637i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28721.3 | − | 49746.8i | −0.931910 | − | 1.61412i | −0.780054 | − | 0.625713i | \(-0.784808\pi\) |
−0.151856 | − | 0.988403i | \(-0.548525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3983.50 | + | 6899.63i | −0.128858 | + | 0.223188i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34019.7 | 1.09380 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34805.7 | 1.11568 | 0.557840 | − | 0.829948i | \(-0.311630\pi\) | ||||
0.557840 | + | 0.829948i | \(0.311630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12340.6 | + | 21374.6i | −0.393190 | + | 0.681026i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28494.8 | − | 49354.4i | −0.905155 | − | 1.56777i | −0.820710 | − | 0.571346i | \(-0.806422\pi\) |
−0.0844449 | − | 0.996428i | \(-0.526912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.i.s.1081.3 | 6 | ||
3.2 | odd | 2 | 1620.4.i.u.1081.3 | 6 | |||
9.2 | odd | 6 | 1620.4.i.u.541.3 | 6 | |||
9.4 | even | 3 | 1620.4.a.f.1.1 | yes | 3 | ||
9.5 | odd | 6 | 1620.4.a.d.1.1 | ✓ | 3 | ||
9.7 | even | 3 | inner | 1620.4.i.s.541.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.d.1.1 | ✓ | 3 | 9.5 | odd | 6 | ||
1620.4.a.f.1.1 | yes | 3 | 9.4 | even | 3 | ||
1620.4.i.s.541.3 | 6 | 9.7 | even | 3 | inner | ||
1620.4.i.s.1081.3 | 6 | 1.1 | even | 1 | trivial | ||
1620.4.i.u.541.3 | 6 | 9.2 | odd | 6 | |||
1620.4.i.u.1081.3 | 6 | 3.2 | odd | 2 |